You are right. Are you actually seriously considering whether to go fully managed or self managed at this point? Pls go AWS route and thank me later :)
I ran through roughly our numbers here [1], it looks like self-hosted costs us about 25% of AWS.
I didn't include labour costs, but the self-hosted tasks (set up of hardware, OS, DB, backup, monitoring, replacing a failed component which would be really unusual) are small compared to the labour costs of the DB generally (optimizing indices, moving data around for testing etc, restoring from a backup).
Yes thank you for that. I always feel like these up front cost analyses miss (or underrate) the ongoing operational cost to monitor and be on call to fix infrastructure when problems occur. But I do find it plausible that the cost savings are such that this can be a wise choice nonetheless.